The French use "Vous êtes fatigués." for a self contained sentence. Here "fatigué" (or fatiguée - feminine) is an adjective and follows the rule of agreement with the subject (here "vous")

You can say "Vous avez fatigué ....." but only as part of a longer sentence → "Vous avez fatigué les enfants".
Here "avez fatigué" is a compound verb using "avoir" so agreement is not required.

Because "avez" is "have", which doesn't make sense in this sentence.

Because that translates to "Are you tired?" whereas "N'es-tu pas fatigué ?" translates to "Aren't you tired?".